Finite Group Databasebeta

← #25139113

Subgroups — #25139113

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583164C211yesmaximal, characteristic, complemented
2#19144216C211yesmaximal, characteristic
3C2×#14583130C211yesmaximal, characteristic, complemented
4#19143290C211yesmaximal, characteristic, complemented
5C22×#13063260C211yesmaximal, characteristic, complemented
6#19135962C211yesmaximal, characteristic, complemented
7#19135952C211yesmaximal, characteristic, complemented
8#19135891C211yesmaximal, characteristic, complemented
9#19135885C211yesmaximal, characteristic, complemented
10#19135497C211yesmaximal, characteristic, complemented
11#19135372C211yesmaximal, characteristic, complemented
12#19135064C211yesmaximal, characteristic, complemented
13#19135058C211yesmaximal, characteristic, complemented
14#19134652C211yesmaximal, characteristic, complemented
15C43×#3056C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22#14583164—24no—
23#14583150—21no—
24#14583147—21no—
25#14583133—21no—
26#14583130—21no—
27#14583130—21no—
28#14583130—21no—
29#14583130—21no—
30#14583130—21no—
31#14582971—21no—
32#14582971—21no—
33D4×C43⋊C8—21no—
34D4×C43⋊C8—21no—
35C2×#13063260—24no—
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39C2×#13063260C2211yescharacteristic
40#14582942C2211yescharacteristic
41C2×#13063256C2211yescharacteristic
42#14582926C2211yescharacteristic
43#14582903C2211yescharacteristic
44#14582900C2211yescharacteristic
45C2×#13063249C2211yescharacteristic
46C2×#13063245C2211yescharacteristic
47C2×#13063244C2211yescharacteristic
48C2×#13063244C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51#14582866C2211yescharacteristic
52#14582863C2211yescharacteristic
53#14582855C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58C2×#137×C43C2211yescharacteristic
59C22×M16×C43C2211yescharacteristic
60C43×#525C2211yescharacteristic
61C2×C22⋊Q8×C43C2211yescharacteristic
62C43×#470—21no—
63C43×#468—21no—
64C43×#467—21no—
65C43×#465—21no—
66C43×#428C2211yescharacteristic
67C43×#419C2211yescharacteristic
68C43×#417C2211yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71#13063350—22no—
72#13063350—41no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—21no—
76C2×#10621884—22no—
77C2×#10621884—22no—
78C2×#10621882—21no—
79#13063332—22no—
80#13063332—22no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—22no—
84C2×#10621877—41no—
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C22×C43⋊C8—22no—
90C22×C43⋊C8—22no—
91C22×C43⋊C8—21no—
92C22×C43⋊C8—21no—
93C22×C43⋊C8D411yescharacteristic
94C22×C43⋊C8D411yescharacteristic
95C22×C43⋊C8D411yescharacteristic
96C22×C43⋊C8D411yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99#13063299—21no—
100#13063299—21no—
101#13063299—21no—
102#13063299—21no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105#13063260—22no—
106#13063260—22no—
107#13063260—22no—
108#13063260D414yescomplemented
109#13063258—21no—
110#13063256—21no—
111#13063256—21no—
112#13063256—21no—
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063246—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063244—22no—
124#13063244—41no—
125#13063241—22no—
126#13063241—41no—
127C22⋊(C43⋊C8)—21no—
128C22⋊(C43⋊C8)—21no—
129C22⋊(C43⋊C8)—21no—
130C22⋊(C43⋊C8)—21no—
131#13063236—21no—
132C4×C43⋊C8—21no—
133C2×#41×C43C2311yescharacteristic
134C22×Q8×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136#137×C43—22no—
137#137×C43—41no—
138C2×Q16×C43—21no—
139C2×SD16×C43—21no—
140C2×M16×C43—21no—
141C2×M16×C43—22no—
142C2×M16×C43—41no—
143C2×M16×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C22×C8×C43—21no—
146#123×C43—21no—
147C22⋊Q8×C43—21no—
148C22⋊Q8×C43—21no—
149C22⋊Q8×C43—21no—
150C22⋊Q8×C43—21no—
151C22⋊Q8×C43D411yescharacteristic
152C22⋊Q8×C43D411yescharacteristic
153#121×C43D411yescharacteristic
154#121×C43D411yescharacteristic
155#120×C43—21no—
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158#117×C43C2311yescharacteristic
159C2×C4⋊C4×C43—21no—
160C2×C4⋊C4×C43C2311yescharacteristic
161C2×C22⋊C4×C43—21no—
162#107×C43—21no—
163#106×C43—21no—
164#103×C43—21no—
165#103×C43—21no—
166#103×C43—21no—
167#102×C43—21no—
168C24×C43#4111yescharacteristic
169C23×D43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43C2×D411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43C2×D411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—82no—
201C22×Dic43—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208Q16×C43—42no—
209SD16×C43—42no—
210M16×C43—21no—
211M16×C43—21no—
212M16×C43—21no—
213M16×C43—42no—
214M16×C43C2×D412yes—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—42no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—41no—
223C4⋊C4×C43—41no—
224C4⋊C4×C43C2×D411yescharacteristic
225C4⋊C4×C43C2×D411yescharacteristic
226C22⋊C4×C43—21no—
227C22⋊C4×C43—21no—
228C22⋊C4×C43—21no—
229C22⋊C4×C43—21no—
230C22⋊C4×C43—21no—
231C22⋊C4×C43—41no—
232C22⋊C4×C43—41no—
233C42×C43—21no—
234#10621884—42no—
235#10621884—42no—
236#10621884—42no—
237#10621882—42no—
238(C2×D43)⋊C4—41no—
239(C2×D43)⋊C4—41no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—21no—
245#10621877—21no—
246#10621877—21no—
247#10621877—21no—
248#10621877—21no—
249#10621877—42no—
250#10621877—42no—
251#10621877C2×D412yes—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—22no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—42no—
263C2×C43⋊C8—42no—
264C2×C43⋊C8C2×D411yescharacteristic
265C2×C43⋊C8C2×D411yescharacteristic
266C2×C43⋊C8C2×D411yescharacteristic
267C2×C43⋊C8C2×D411yescharacteristic
268C2×C43⋊C8C2×D412yes—
269C2×C43⋊C8#4112yes—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—22no—
273C23×C43—21no—
274C23×C43—41no—
275C23×C43#12111yescharacteristic
276C23×C43#12111yescharacteristic
277C23×C43C2×#4111yescharacteristic
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—41no—
281C22×D43—81no—
282C22×D43—81no—
283Q8×C43—21no—
284Q8×C43—21no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—41no—
288Q8×C43—41no—
289D4×C43—21no—
290D4×C43—21no—
291D4×C43—42no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—42no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—81no—
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4111yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C432−1+411yescharacteristic
323C22⋊D43—82no—
324C22⋊D43—82no—
325C2×Dic43—41no—
326C2×Dic43—81no—
327D172—41no—
328D172—41no—
329D172—41no—
330D172—41no—
331C8×C43—22no—
332C8×C43—41no—
333C43⋊C8—21no—
334C43⋊C8—21no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339C43⋊C8#12112yes—
340C43⋊C8#12112yes—
341#24802—431nomaximal, Sylow
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—21no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43#47112yescomplemented
355C22×C43C2×#12111yescharacteristic
356C22×C43#54811yescharacteristic
357C22×C43#55311yescharacteristic
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—161no—
362C2×D43—161no—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—41no—
368C4×C43—81no—
369C4×C43—81no—
370C4×C43C2×#12111yescharacteristic
371C4×C43#53711yescharacteristic
372C4×C43D4211yescharacteristic
373C4×C43#54711yescharacteristic
374Dic43—81no—
375C2×#471—431no—
376#3056D4311yescharacteristic, complemented
377#3055—431no—
378C2×#465—431no—
379#2929—431no—
380C22×#108—431no—
381#2064—431no—
382#2063—431no—
383#2052—431no—
384#2051—431no—
385#1977—431no—
386#1951—431no—
387#1901—431no—
388#1900—431no—
389#1815—431no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—22no—
393C2×C43—41no—
394C2×C43—81no—
395C2×C43#241611yescharacteristic
396C2×C43C2×#47111yescharacteristic
397C2×C43#306711yescharacteristic
398D43—161no—
399C2×#137C2×D4311yescharacteristic
400C2×AGL(1,ℤ/8)—431no—
401C22×SD16—431no—
402C2×#131—431no—
403C22×M16—431no—
404C22×M16C2×D4311yescharacteristic
405C23×C8—431no—
406#525C2×D4311yescharacteristic
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×#121—431no—
409#471—864no—
410#470—21no—
411#469—861no—
412#468—21no—
413#468—861no—
414#467—21no—
415#466—861no—
416#465—21no—
417#465—861no—
418#465—861no—
419#465—861no—
420#465—861no—
421#465—861no—
422#435—861no—
423#435—861no—
424C8×D4—861no—
425C8×D4—861no—
426C2×#108—431no—
427C2×#108—431no—
428C2×#108—431no—
429C2×#108—431no—
430C2×#108—864no—
431#428—431no—
432#428C2×D4311yescharacteristic
433C2×#106—431no—
434#424—431no—
435#419C2×D4311yescharacteristic
436#418—431no—
437#417—431no—
438#417C2×D4311yescharacteristic
439C2×#103—431no—
440C2×#102—431no—
441C2×#101—431no—
442C2×#101—431no—
443C2×#100—431no—
444C2×#100—431no—
445#408—431no—
446#407—431no—
447#405—431no—
448#343—431no—
449#343—431no—
450#343—431no—
451#343—431no—
452C43#2480211yescharacteristic, complemented, Sylow
453C2×#41C22×D4311yescharacteristic
454C22×Q8C22×D4311yescharacteristic
455C22×D4—431no—
456C22×D4—861no—
457C23×C4C22×D4311yescharacteristic
458#137—22no—
459#137—41no—
460AGL(1,ℤ/8)—862no—
461AGL(1,ℤ/8)—1721no—
462C2×Q16—21no—
463C2×SD16—21no—
464C2×SD16—862no—
465C2×SD16—861no—
466C2×SD16—861no—
467C2×SD16—862no—
468C2×SD16—861no—
469C2×D8—861no—
470#131—862no—
471#131—862no—
472C2×M16—21no—
473C2×M16—22no—
474C2×M16—41no—
475C2×M16—431no—
476C2×M16—431no—
477C2×M16—431no—
478C2×M16—431no—
479C2×M16—861no—
480C2×M16—861no—
481C2×M16—862no—
482C2×M16—1721no—
483C2×M16C22×D4311yescharacteristic
484C2×M16C22×D4311yescharacteristic
485C22×C8—21no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—431no—
492C22×C8—862no—
493C22×C8—862no—
494C22×C8—861no—
495C22×C8—861no—
496#123—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8C22⋊D4311yescharacteristic
502C22⋊Q8C22⋊D4311yescharacteristic
503#121—861no—
504#121—861no—
505#121—861no—
506#121—861no—
507#121C22⋊D4311yescharacteristic
508#121C22⋊D4311yescharacteristic
509#120—21no—
510C4×D4—21no—
511C4×D4—21no—
512#117C22×D4311yescharacteristic
513C2×C4⋊C4—21no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—861no—
518#108—434no—
519#108—862no—
520#108—862no—
521#108—862no—
522#107—21no—
523#107—861no—
524#106—21no—
525#106—861no—
526#106—861no—
527#106—861no—
528C4⋊C8—861no—
529C4⋊C8—861no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—861no—
534#103—861no—
535#103—861no—
536#102—21no—
537#102—861no—
538#102—861no—
539#102—861no—
540#102—861no—
541#102—861no—
542#101—862no—
543#101—1721no—
544#100—862no—
545#100—1721no—
546C22⋊C8—861no—
547C22⋊C8—861no—
548C22⋊C8—861no—
549C22⋊C8—861no—
550#97—861no—
551C4×C8—861no—
552C24—861no—
553C24#1062190011yescharacteristic
554#41—21no—
555#41—21no—
556#41—21no—
557#41—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×C22⋊D4311yescharacteristic
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—861no—
574C2×D4—3442no—
575C2×D4—1721no—
576C2×D4—1721no—
577C2×D4C2×C22⋊D4311yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—861no—
586C22×C4D4×D4311yescharacteristic
587C22×C4D4×D4311yescharacteristic
588C22×C4#1062190011yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592Q16—42no—
593SD16—42no—
594SD16—1722no—
595SD16—1722no—
596SD16—1722no—
597D8—1722no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16—42no—
602M16—432no—
603M16—861no—
604M16—861no—
605M16—861no—
606M16—861no—
607M16—861no—
608M16—861no—
609M16—861no—
610M16—1722no—
611M16—1722no—
612M16D4×D4312yes—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—42no—
616C2×C8—431no—
617C2×C8—431no—
618C2×C8—432no—
619C2×C8—432no—
620C2×C8—431no—
621C2×C8—431no—
622C2×C8—862no—
623C2×C8—862no—
624C2×C8—862no—
625C2×C8—862no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—1722no—
633C2×C8—1722no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4C2×C22⋊D4311yescharacteristic
643C4⋊C4C2×C22⋊D4311yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—1721no—
652C22⋊C4—1721no—
653C42—21no—
654C23—21no—
655C23—21no—
656C23—22no—
657C23—21no—
658C23—41no—
659C23—3441no—
660C23—3441no—
661C23—1721no—
662C23—1721no—
663C23—1721no—
664C23#1306329711yescharacteristic
665C23#1306329711yescharacteristic
666C23C2×#1062190011yescharacteristic
667Q8—21no—
668Q8—21no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673D4—21no—
674D4—21no—
675D4—42no—
676D4—41no—
677D4—41no—
678D4—42no—
679D4—3442no—
680D4—3442no—
681D4—1721no—
682D4—1721no—
683D4—1721no—
684D4—1721no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—81no—
705C2×C4—3441no—
706C2×C4—1721no—
707C2×C4#1306329711yescharacteristic
708C2×C4#1306329711yescharacteristic
709C2×C4C2×D4×D4311yescharacteristic
710C2×C4C2×D4×D4311yescharacteristic
711C2×C4C22×C22⋊D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4#1306337011yescharacteristic
714C2×C4#1306337211yescharacteristic
715C8—22no—
716C8—41no—
717C8—432no—
718C8—432no—
719C8—861no—
720C8—861no—
721C8—862no—
722C8—1721no—
723C8—1721no—
724C8—1721no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—3441no—
738C22—3441no—
739C22—3441no—
740C22—6881no—
741C22—6881no—
742C22#1458316412yescomplemented
743C22C2×#1306329711yescharacteristic
744C22#1458355511yescharacteristic
745C22#1458359211yescharacteristic
746C4—21no—
747C4—21no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—3441no—
754C4#121×D4311yescharacteristic
755C4#1458347611yescharacteristic
756C4D4×C22⋊D4311yescharacteristic
757C4#1458354811yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—6881no—
764C2#1913803211yescharacteristic
765C2C2×#1458316411yescharacteristic
766C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3056C2
socleC22×C43C2×#121
prime radical#19144216C2
hypercenter#3056D43
hypocenterC43#24802
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3056

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14583164C2semidirect
3. C2×#14583130C2semidirect
4. #19143290C2semidirect
5. C22×#13063260C2semidirect
6. #19135962C2semidirect
7. #19135952C2semidirect
8. #19135891C2semidirect
9. #19135885C2semidirect
10. #19135497C2semidirect
11. #19135372C2semidirect
12. #19135064C2semidirect
13. #19135058C2semidirect
14. #19134652C2semidirect
15. C43×#3056C2semidirect
108. #13063260D4semidirect
354. C22×C43#471semidirect
376. #3056D43semidirect
452. C43#24802semidirect
742. C22#14583164semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145831642
#191442162
C2×#145831302
#191432902
C22×#130632602
#191359622
#191359522
#191358912
#191358852
#191354972
#191353722
#191350642
#191350582
#191346522
C43×#30562
#2480243